I: (50 percent)
Do you agree with the following statements? Explain why or why not.
a:
‘An increase in government consumption has no effects on growth as long as
the government always runs a balanced budget.’
b:
‘Governments should subsidize private research and development activities
(R&D) in order to give firms stronger incentives to engage in R&D’.
c:
‘The neo-classical growth model predicts that there will be instantaneous
convergence between countries with access to international credit.’
II: (50 percent)
Consider an economy where total production, Y , is given by a neo-classical
production function
Y = F(K, TL) (1)
Here K is the aggregate capital-stock, L is the size of the population/workforce,
and T is a parameter characterizing the level of technology. Assume
that T and L grow exogenously at rates g and n, respectively. Define ˆy ≡
Y/(TL) and ˆk ≡ K/(TL).
a) Explain, intuitively, why ˆk converges to a steady state ˆk∗
in neo-classical
growth models.
—
Let the evolution of ˆk over time (t) be approximated by the log-linearization
dˆk(t)/dt
ˆk(t)
= λ(ln ˆk∗
− ln ˆk(t)) (2)
Based on (2), it follows that
dˆy(t)/dt
ˆy(t)
= λ(ln ˆy∗
− ln ˆy(t)), (3)
1
which in turn implies
ln ˆy(t) − ln ˆy(0)
t
= b1 ln ˆy∗
− b2 ln ˆy(0) (4)
where b1 = b2 = (1 − e−λt
)/t. (You do not need to prove these results).
b) In the framework of a simple Solow-model: Illustrate and explain the
relationship (2) graphically. (You do not need to derive the equation alge-
braically).
c) Explain the difference between i) absolute convergence across economies
and ii) conditional convergence across economies.
—
Now let the production function (5) be replaced by
Y = F(K, H, TL) = Kα
Hη
(TL)1−α−η
(5)
where H is the aggregate stock of human capital. Assume that K and H
are both produced by the same technology as Y , that they depreciate at the
common rate δ, and that fixed shares sk and sh of total production are used
to invest in K and H respectively.
Under these assumptions it can be shown that the steady state value ˆy∗
satisfies
ln(ˆy∗
) =
α
1 − α − η
ln(sk) +
η
1 − α − η
ln(sh) −
α + η
1 − α − η
ln(n + g + δ) (6)
and that the log-linearization for the evolution of ˆy is
dˆy(t)/dt
ˆy(t)
= (1 − α − η)(n + g + δ)(ln ˆy∗
− ln ˆy(t)), (7)
i.e. as in (3), but with
λ = (1 − α − η)(n + g + δ) (8)
(Again: You do not need to prove these results).
d) State a rough estimate of what you consider plausible values for λ? What
does this measure say about how quickly economies converge?
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e) Show that under the assumptions of the augmented model, equation (4)
translates to
ln(y(t)) − ln(y(0))
t
=
(1 − e−λt
)
t
α
1 − α − η
ln(sk) +
(1 − e−λt
)
t
η
1 − α − η
ln(sh)
−
(1 − e−λt
)
t
α + η
1 − α − η
ln(n + g + δ) −
(1 − e−λt
)
t
ln(y(0))
+
(1 − e−λt
)
t
ln T(0) + gt
f) Consider the estimation results reported in Tables IV and V in the appendix
on the next page (taken from the study by Mankiw, Romer and Weil
1992). What do these results tell us about the model discussed above? (You
may focus on the intermediate sample.)
g) What are the main weaknesses of the analysis leading to the results in
Tables IV and V? (Explain briefly, but without going in detail on each point).
h) Discuss briefly other approaches for studying the relationship (4) empiri-
cally.
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Appendix
Regression results from Mankiw, Romer and Weil (1992)
4